2 min readโขnovember 3, 2020

Peter Apps

Electric Potential Energy can also be expressed in terms of the Electric Field Strength

Review Note: Conservation of Energy applies here too!

Let's take a closer look at that last energy equation we derived. Rearranging it a bit, we get:

The left-hand side of this equation shows the work (or amount of energy) per unit of charge. This "work per charge" quantity is called electric potential or voltage (V).

W or Ue is electric potential energy, measured in Joules. It is NOT the same as potential difference, V, measured in Joules/Coulomb.

Like energy, voltage is a SCALAR. The change may be positive or negative, but that doesn't imply directionality!

Electric Potential of a Point Charge

Since the electric field strength decreases as the radius increases, the voltage must also be decreasing as we travel further away from the charge.

We can determine the change in voltage by doing some calculus. Let's imagine traveling away from the charge from radius a to radius b.

Try using the PhET simulation to create your own fields and notice the how the voltage and equipotential lines change as a function of charge and distance.

Image from Wikipedia

Image from openstax.org

1.

Image from Collegeboard.org

2.

Image from Collegeboard.org

Answer:
a) The Electric Field Lines point from high potential to low potential and are perpendicular to the equipotential lines. Therefore at point A, the electric field line points up and to the right

b) E is the greatest where the V lines are closest together (largest gradient). This happens at B.

c)

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